Question

The number of hits to a website follows a Poisson process. Hits occur at the rate of 2.9 per minute between 7:00 P.M. and

11:00 P.M. Given below are three scenarios for the number of hits to the website. Compute the probability of each scenario between 8 : 44 P.M.

and 8:46 P.M. Interpret each result.

(a) exactly six

(b) fewer than six

(c) at least six

Answer #1

The number of hits on website follows Poisson process: It's probability is:

P(x) = e-λt*(λt)x/x!

Hits occurrence rate = 2.9 per min

And random variable x is defined over the interval between 8:44 PM and 8:46 PM, so t = 2 minutes

**Answer a)**

Probability of exactly six

P(6) = e-2.9*2*(2.9*2)6/6!

P(6) = **0.1601**

**Answer b)**

Probability of fewer than six

P(x < 6) = P(0) + P(1) + P(2) + P(3) + P(4) + P(5)

P(0) = e-2.9*2*(2.9*2)0/0! = 0.0030

P(1) = e-2.9*2*(2.9*2)1/1! = 0.0176

P(2) = e-2.9*2*(2.9*2)2/2! = 0.0509

P(3) = e-2.9*2*(2.9*2)3/3! = 0.0985

P(4) = e-2.9*2*(2.9*2)4/4! = 0.1428

P(5) = e-2.9*2*(2.9*2)5/5! = 0.1656

P(x < 6) = 0.0030 + 0.0176 + 0.0509 + 0.0985 + 0.1428 + 0.1656

P(x < 6) = **0.4784**

**Answer c)**

Probability of at least six

P(x ≥ 6) = 1 - P(x < 6) = 1 - 0.4784

P(x ≥ 6) = **0.5216**

The number of hits to a website follows a Poisson process. Hits
occur at the rate of 1.0 per minute between 7:00 P.M. and 12:00
P.M. Given below are three scenarios for the number of hits to the
website. Compute the probability of each scenario between 7 : 29
P.M. and 7:34 P.M. Interpret each result.
(a) exactly eight
(b) fewer than eight
(c) at least eight
(a) P(8)=___ (Round to four decimal places as needed.)

The number of hits to a website follows a Poisson process. Hits
occur at the rate of 1.8 per minute between 7:00 P.M. and 9:00
P.M. Given below are three scenarios for the number of hits to the
website. Compute the probability of each scenario between 7 : 43
P.M. and 7:48 P.M.
Interpret each result.
(a) exactly eight (
b) fewer than eight
(c) at least eight
(a) P(8) =______ (Round to four decimal places as
needed.)...

The number of hits to a Web site follows a Poisson process. Hits
occur at the rate of 0.8 per minute between 7:00 P.M. and 11:00
P.M. Given below are three scenarios for the number of hits to the
Web site. Compute the probability of each scenario between 8 : 39
P.M. and 8:48 P.M. and interpret the results.
(a) exactly seven hits
(b) fewer than seven hits
(c) at least seven hits

The number of hits to a website follows a Poisson process. Hits
occur at the rate of 2.1 per minute 2.1 per minute between 7:00
P.M. and 11:00PM. Given below are three scenarios for the number
of hits to the website. Compute the probability of each scenario
between 10:44 P.M. and 10:50 P.M. Interpret each result.
(a) exactly six
(b) fewer than six
(c) at least six
(a) P(6)= _____
On about _____of every 100 time intervals between 10:44 P.M....

The number of hits to a Web site follows a Poisson process. Hits
occur at the rate of 1.9 per minute1.9 per minute between 7:00
P.M. and 9:00 P.M. Given below are three scenarios for the number
of hits to the Web site. Compute the probability of each scenario
between .7:41 P.M. and 7:45 P.M.
(a) exactly six.
(b) fewer than six
(c) at least six.

The number of hits to a Web site follows a Poisson process. Hits
occur at the rate of 1.2 per minute between 7pm and 12 pm. Given
below are three scenarios for the number of hits to the Website.
Compute the probabilityof each scenario between 8:21pm and
8:24pm.
a. exactly six
b. fewer than six
c. at least six

Hi, Please disregard the first question I asked the same like
this. This is the updated one.
Please answer the problem below.
Thank you,
The number of hits to a website follows a Poisson process. Hits
occur at the rate of 0.9 per minute between 7:00 P.M. and 11:00
P.M. Given below are three scenarios for the number of hits to the
website. Compute the probability of each scenario between 10 : 33
P.M. and 10:43 P.M. Interpret each result....

The number of traffic accidents in a certain area follows a
Poisson process with a rate of 1.5 per hour between 8:00 A.M. and
5:00 P.M. during the normal working hours in a working day. Compute
the following probabilities.
There will be no traffic accident between 11:30 AM to 12:00
PM.
There will be more than 3 traffic accidents after 3:45
P.M.
There will be in between 15 and 18 traffic accident during the
normal working hours in a working...

You have observed that the number of hits to your web site
follows a Poisson distribution at a rate of 3 per hour. Let X is
the time between hits and it follows Exponential distribution.
1. What is an average time in minutes between two hits?
2. What is the probability, that you will need to wait less than
40 minutes between two hits?
3. What is the probability, that there will be 2 hits in the
next hour?
1....

(a) Consider a certain newspaper article on the website of the
newspaper. The number of hits that article gets, from the Weblog of
the newspaper server, follows a Poisson distribution with a
parameter (λ) of one (1) hit per four (4) hour slots. The Web
server is online the whole day.
(i)Determine the probability that an article will have at least
one (1) hit in a day.
(ii) The server contains 25 such articles. Determine the
probability that at least...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 10 minutes ago

asked 17 minutes ago

asked 29 minutes ago

asked 29 minutes ago

asked 43 minutes ago

asked 51 minutes ago

asked 55 minutes ago

asked 56 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago